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Answer :
Final answer:
The rocket will reach its maximum height 1 second after launch. The maximum height of the rocket is 57 feet.
Explanation:
To find the time it takes for the rocket to reach its maximum height, we need to find the vertex of the quadratic function representing the height of the rocket. The vertex of a quadratic function in the form h(t) = at^2 + bt + c is given by t = -b / (2a). In this case, a = -16 and b = 32, so t = -32 / (2*-16) = 1. The rocket will reach its maximum height 1 second after launch.
To find the maximum height, we substitute the time t = 1 into the height function h(t) = -16t^2 + 32t + 9. Therefore, h(1) = -16(1)^2 + 32(1) + 9 = 16 + 32 + 9 = 57 feet. The maximum height of the rocket is 57 feet.
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